On the Efficiency of Pollard's Rho Method for Discrete Logarithms

Bai, S. and Brent, R.P.

Pollard's rho method is a randomized algorithm for
computing discrete logarithms. It works by defining a
pseudo-random sequence and then detecting a match
in the sequence. Many improvements have been proposed,
while few evaluation results and efficiency suggestions
have been reported. This paper is devoted
to a detailed study of the efficiency issues in Pollard's
rho method. We describe an empirical performance
analysis of several widely applied algorithms. This
should provide a better combination of algorithms
and a good choice of parameters for Pollard's rho
method.